Long multiplication: Difference between revisions

=={{header|Quackery}}==

Long multiplication as it was taught at primary school, using natural numbers (including zero) in the base 10 numeral system, with a slight variation in that it maintains a running total rather than adding up the intermediate results column-wise at the end. Starting point is "learn your tables". Presumptions are an understanding of "equal to" and "not equal to", and the ability to split a one or two digit number into tens and units.

(This is achieved using <code>/mod</code> to keep the tables compact. Numbers in the addition and multiplication tables could be represented as, for example, <code>[ 8 1 ]</code> instead of <code>81</code> and <code>10 /mod</code> replaced with <code>unpack</code> or, as the nest only contains numbers, <code>do</code>.)

In addition to the specified task, we were always encouraged to show our workings.

<lang Quackery> [ [] swap witheach

[ char 0 -

swap join ] ] is $->long ( $ --> L )

[ number$ $->long ] is long ( n --> L )

[ reverse behead

swap witheach

[ swap 10 * + ] ] is long->num ( L --> n )

[ reverse

witheach echo ] is echolong ( L --> )

[ over size

over size -

dup dip

[ 0 < if swap ]

abs times

[ 0 join ] ] is zeropad ( L L --> L L )

[ [ table

[ 0 1 2 3 4 5 6 7 8 9 ]

[ 1 2 3 4 5 6 7 8 9 10 ]

[ 2 3 4 5 6 7 8 9 10 11 ]

[ 3 4 5 6 7 8 9 10 11 12 ]

[ 4 5 6 7 8 9 10 11 12 13 ]

[ 5 6 7 8 9 10 11 12 13 14 ]

[ 6 7 8 9 10 11 12 13 14 15 ]

[ 7 8 9 10 11 12 13 14 15 16 ]

[ 8 9 10 11 12 13 14 15 16 17 ]

[ 9 10 11 12 13 14 15 16 17 18 ] ]

swap peek 10 /mod ] is add ( n n --> n n )

[ dip add add dip [ add nip ] swap ] is addc ( n n c --> n c )

[ zeropad

0 temp put

[] unrot witheach

[ dip behead

temp take

addc

temp put

rot swap join swap ]

drop

temp take dup 0 !=

iff join else drop ] is longadd ( L L --> L )

[ [ table

[ 0 0 0 0 0 0 0 0 0 0 ]

[ 0 1 2 3 4 5 6 7 8 9 ]

[ 0 2 4 6 8 10 12 14 16 18 ]

[ 0 3 6 9 12 15 18 21 24 27 ]

[ 0 4 8 12 16 20 24 28 32 36 ]

[ 0 5 10 15 20 25 30 35 40 45 ]

[ 0 6 12 18 24 30 36 42 48 54 ]

[ 0 7 14 21 28 35 42 49 56 63 ]

[ 0 8 16 24 32 40 48 56 64 72 ]

[ 0 9 18 27 36 45 54 63 72 81 ] ]

swap peek 10 /mod ] is mult ( n n --> n n )

[ dip mult add dip [ add nip ] swap ] is multc ( n n c --> n c )

[ dup 0 = iff

[ 2drop 0 long ] done

0 temp put

[] unrot swap witheach

[ over temp take

multc

temp put

swap dip join ]

drop

temp take dup 0 !=

iff join else drop ] is shortmult ( L n --> L )

[ ' [ 0 ] over != iff

[ 0 swap join ] ] is timesten ( L --> L )

[ dup 0 long = iff

[ 2drop 0 long ] done

0 long unrot

witheach

[ dip dup shortmult

rot longadd swap

timesten ]

drop ] is longmult ( L L --> L )

( ------------------------ additional to task ------------------------ )

[ stack ] is linelength ( --> s )

[ linelength share times

[ char - emit ]

cr ] is separator ( --> )

[ linelength share

over size - times sp

echolong cr ] is showlong ( --> )

[ over size

over size + linelength put

over showlong

dup showlong

separator

dup 0 long = iff

[ 2drop 0 long ] done

0 long unrot

witheach

[ dip dup shortmult

dup showlong

rot longadd swap

timesten ]

separator

swap showlong

separator

drop linelength release ] is workings ( L L --> )

say "Using long multiplication: "

2 64 ** long dup longmult dup echolong cr

say "Using built-in arithmetic: "

2 128 ** dup echo cr cr

swap long->num = iff

say "10/10, Gold star!"

else

say "0/10, See me after class."

cr cr

say "(Show your workings.)" cr cr

2 64 ** long dup workings cr</lang>

{{out}}

<pre>Using long multiplication: 340282366920938463463374607431768211456

Using built-in arithmetic: 340282366920938463463374607431768211456

10/10, Gold star!

(Show your workings.)

18446744073709551616

18446744073709551616

----------------------------------------

110680464442257309696

184467440737095516160

11068046444225730969600

18446744073709551616000

922337203685477580800000

9223372036854775808000000

166020696663385964544000000

0

12912720851596686131200000000

55340232221128654848000000000

1291272085159668613120000000000

0

73786976294838206464000000000000

737869762948382064640000000000000

12912720851596686131200000000000000

110680464442257309696000000000000000

737869762948382064640000000000000000

7378697629483820646400000000000000000

147573952589676412928000000000000000000

184467440737095516160000000000000000000

----------------------------------------

340282366920938463463374607431768211456

----------------------------------------</pre>